Given, relation R on N is defined by R={(x,y)∈N×N:x3−3x2−xy2+3y3=0} x3−3x2y−xy2+3y3=0 ⇒x3−xy2−3x2y+3y3=0 ⇒x(x2−y2)−3y(x2−y2)=0 ⇒(x−3y)(x2−y2)=0 ⇒(x−3y)(x−y)(x+y)=0 Now, x−x=0 ⇒x=x,∀(x,x)∈N×N So, R is a reflexive relation. But not symmetric and transitive relation because, (3,1) satisfies but (1,3) does not. Also, (3,1) and (1,−1) satisfies but (3,−1) does not. Hence, relation R is reflexive but neither symmetric nor transitive.